{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T02:29:21Z","timestamp":1780972161093,"version":"3.54.1"},"reference-count":9,"publisher":"Cambridge University Press (CUP)","issue":"A","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2014,12]]},"abstract":"<jats:p>Consider a bipartite random geometric graph on the union of two independent homogeneous Poisson point processes in <jats:italic>d<\/jats:italic>-space, with distance parameter <jats:italic>r<\/jats:italic> and intensities \u03bb and \u03bc. We show for <jats:italic>d<\/jats:italic> \u2265 2 that if \u03bb is supercritical for the one-type random geometric graph with distance parameter 2<jats:italic>r<\/jats:italic>, there exists \u03bc such that (\u03bb, \u03bc) is supercritical (this was previously known for <jats:italic>d<\/jats:italic> = 2). For <jats:italic>d<\/jats:italic> = 2, we also consider the restriction of this graph to points in the unit square. Taking \u03bc = \u03c4 \u03bb for fixed \u03c4, we give a strong law of large numbers as \u03bb \u2192 \u221e for the connectivity threshold of this graph.<\/jats:p>","DOI":"10.1017\/s0021900200021367","type":"journal-article","created":{"date-parts":[[2016,3,30]],"date-time":"2016-03-30T16:25:31Z","timestamp":1459355131000},"page":"333-344","source":"Crossref","is-referenced-by-count":2,"title":["Continuum AB percolation and AB random geometric graphs"],"prefix":"10.1017","volume":"51","author":[{"given":"Mathew D.","family":"Penrose","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2016,3,30]]},"reference":[{"key":"S0021900200021367_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2013.03.022"},{"key":"S0021900200021367_ref8","first-page":"6","volume":"76","year":"2007","journal-title":"Phys. Rev. E"},{"key":"S0021900200021367_ref7","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2011.2173726"},{"key":"S0021900200021367_ref6","volume-title":"Random Geometric Graphs","year":"2003"},{"key":"S0021900200021367_ref1","first-page":"1182","volume":"10","year":"2000","journal-title":"Ann. Appl. Prob."},{"key":"S0021900200021367_ref4","first-page":"3659","volume":"114","year":"2000","journal-title":"J. Chem. Phys."},{"key":"S0021900200021367_ref3","doi-asserted-by":"publisher","DOI":"10.1239\/aap\/1331216643"},{"key":"S0021900200021367_ref2","volume-title":"Percolation","year":"1999"},{"key":"S0021900200021367_ref5","volume-title":"Continuum Percolation","year":"1996"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900200021367","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,4,22]],"date-time":"2017-04-22T11:36:13Z","timestamp":1492860973000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900200021367\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,12]]},"references-count":9,"journal-issue":{"issue":"A","published-print":{"date-parts":[[2014,12]]}},"alternative-id":["S0021900200021367"],"URL":"https:\/\/doi.org\/10.1017\/s0021900200021367","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,12]]}}}